A multi-factor model with time-varying and seasonal risk premiums for the natural gas market Chengwu Shao a , Ramaprasad Bhar b, ⁎, David B. Colwell a a School of Banking and Finance, Business School, The University of New South Wales, Sydney, NSW 2052, Australia b School of Risk and Actuarial, Business School, The University of New South Wales, Sydney, NSW 2052, Australia abstract article info Article history: Received 16 June 2014 Received in revised form 26 February 2015 Accepted 24 April 2015 Available online 2 May 2015 JEL classification: Q40 Q43 G13 C32 Keywords: Natural gas Short-term and long-term factors Risk premium Seasonality In this paper, we develop a quantitative model of the US natural gas market that explores its multi-factor structure and its time-varying and seasonal risk premiums. With weekly spot and futures prices we show that three factors are preferred to describe the futures term structure, and the time-varying risk premiums are also significant. Moreover, we found that the market implies a seasonal risk premium with two peaks and troughs in one year, which is important to correctly price the futures by maturity month. Finally, we link this seasonal risk premium to the uncertainty of the US natural gas demand and find a positive relationship between them. These results reveal the complex aspect of the market, and may have useful applications for other commodity sectors. © 2015 Published by Elsevier B.V. 1. Introduction Global natural gas markets have undergone significant changes in regulation in recent decades. The US natural gas market is now the largest one in the world and its deregulation started with The Natural Gas Policy Act in 1978. Since then, the market has become more competitive and relevant trading activities have greatly increased. Therefore it is impor- tant for both academia and industry to obtain a deep understanding of price movements and risk factors in the market. The spot-based commodity models trace back to Brennan and Schwartz (1985). This early model does not consider the mean- reversion phenomenon and the Samuelson effect (i.e., the observation that the volatility of a commodity futures contract tends to increase when approaching its maturity) which are two properties usually seen in commodity markets, including natural gas. To incorporate these properties, Schwartz (1997) proposed a one-factor model where the spot log-price follows an Ornstein–Uhlenbeck process. However, the futures term structures derived under this model are too strict and inconsistent with empirical observations. In fact, the futures prices over the whole term curve are perfectly correlated. Moreover, the futures price volatility shrinks to zero in the long term, which is not the case in reality. To solve these drawbacks, several two-factor models have been con- structed in the literature. Broadly speaking these models can be divided into two types. The first type is based on Gibson and Schwartz (1990) where one factor is the spot price and the other is the stochastic conve- nience yield. The second type was introduced in Schwartz and Smith (2000) where one factor models short-term price deviations and the other models the long-term equilibrium price evolution (hereafter ST/LT). Schwartz and Smith also showed that both types are equivalent in nature. Under these models the futures prices are no longer perfectly correlated and so richer term structures can be produced. In addition, because of the long-term factor, the futures price volatility converges to a non-zero value in the long term, which is closer to actual situations. Between the two types, the Schwartz and Smith (2000) structure has advantages of being easy to interpret and having usually weakly corre- lated factors. Since then, a number of papers have extended the original ST/LT model to three factors by adding another short-term factor (hereafter 2ST/LT) and found evidence in favour of such an extension. Cortazar and Naranjo (2006) developed a general N-factor framework and found that the 2ST/LT model fits the crude oil futures term struc- ture much better than the ST/LT model. Bhar and Lee (2011) also conducted a model comparison using crude oil futures. They found that the 2ST/LT model shows significant improvement and the ST/LT Energy Economics 50 (2015) 207–214 ⁎ Corresponding author. Tel.: +61 2 9385 4930. E-mail addresses: c.shao@student.unsw.edu.au (C. Shao), r.bhar@unsw.edu.au (R. Bhar), d.colwell@unsw.edu.au (D.B. Colwell). http://dx.doi.org/10.1016/j.eneco.2015.04.013 0140-9883/© 2015 Published by Elsevier B.V. Contents lists available at ScienceDirect Energy Economics journal homepage: www.elsevier.com/locate/eneco